Everyone knows that real people suck at coming up with strong passwords. They are either easy to remember and laughably weak, or decently strong and impossible
to recall. On top of that, it is highly recommended to use different passwords for different sites, so that compromising one won’t compromise the others. In this article, I follow Nobel laureate Manuel Blum’s recommendation of using not a password, but an easy to remember algorithm to come up with a way to generate strong, specific passwords for each site, and be able to remember them all.
In this talk, Manuel Blum asks four volunteers from the audience, who we presume not to have been prepared before the lecture, and explains to them a method which, when given a name to apply it to, leads them all to the same, apparently random result. The video does not reveal the method used, but some articles by Blum speak about mapping the alphabet (plus numbers) into a secret scrambled grid, and applying a secret walk to the successive letters of the name (presumably a website name) to be converted into something else. Thus, the user only needs to memorize the scrambled alphabet and the steps taken in the walk.
I don’t think I could do that, though, so here’s my counter-proposal: use the computer keyboard as my grid, and just memorize the method, plus maybe a simple code that I can change from time to time. Let’s say I want to come up with a strong password for amazon.com. I start, therefore, from the word “amazon”, which I am going to turn into something else. In order to increase security, I memorize the secret code “1234” (maybe I can’t memorize a scrambled alphabet, but this I can memorize). Now I do the following on an American qwerty keyboard like this:
- Starting with the first letter in the original word, move down (and slightly to the right) on the keyboard as many keys as the first digit of the code. If this causes me to fall off the lower edge, I continue on the top row, on the key directly above the last one I touched. Since the first letter is “a” and the first digit is “1”, I move one key down from “a”, which is “z”.
- Repeat with the second letter of the name and the second digit, then do the same until all the letters have been transformed. If I run out of numbers, I take the first number again, and so on. Therefore the other letters are:
- “m” + 2 = “i” (wrap to “8” on the first step, and then down to “i”)
- “a” + 3 = “w” (wrap from “z” to “2” on the second step, and then down to “w”)
- “z” + 4 = “x” (wrap from “z” to “2” on the first step, and then down to “x”)
- “o” + 1 = “l” (observe that we go back to “1”, since we ran out of digits on the key)
- “n” + 2 = “u” (wrap from “n” to “7” on the first step, and then down to “u”)
Final result: “ziwxlu”, which likely does not appear in any dictionary and is therefore as hard to crack as a group of random letters. If the website demands that you add numbers, go ahead and add a few that you can easily remember (except “1234”, which would compromise the key). This time I will add “1111”, making the final password “ziwxlu1111”. Never mind that the numerical part is weak; the strength is in the first part, which is one out of 366 = 2,176,782,336 possibilities (numbers are also part of the set).
What we have done is essentially to apply the Vigenère encryption algorithm to the word “amazon”, using “1234” as key and the qwerty keyboard read column by column as starting alphabet. Not secure by today’s standards, but again, we are using it to generate a password, which itself has a small probability of being revealed. Additionally, anyone having access to the password will still have to figure out the algorithm, since what I’ve presented above is just a sample. There are many other ways you can apply a key to a website name. For instance:
- Do as above but instead moving up, or left, or right on the keyboard. Or maybe alternating directions, or even switching directions in a more complex pattern that is still easy to remember: a cross, a circle, etc.
- Use an alphanumerical key, and then find the result key by doing a “Playfair” combination. In the classic Playfair cipher, two letters at a time combine into one, this way: if there are in the same row or column, take the letter following the first, right or down respectively, depending on whether they are on the same row (or is the same letter) or column. If they are on different row and column, trace a rectangle with the two letters as opposite corners, and then choose the upper new corner (or lower, or right, or left) as result. For instance: “”q” + “t” = “w” (same row), “r” + “v” = “f” (same column), “i” + “c” = “e” (neither). This method also can be subject to direction changes, if so desired.
- Use no key at all, and just rely on direction changes to get the result. For instance, Blum used a one-step north-east-south-west repeating walk, which would turn “amazon” into “q,z/9m” on the qwerty keyboard, excluding non-character keys and the space bar.
There are several reasons why this method, even when not using a key at all, is easier and more secure than others.
- It is certainly easier than having to remember Blum’s secret square containing a scrambled alphabet. The keyboard is there, so why not use it? Otherwise, I might feel tempted to write down the square on a piece of paper because it is hard to do the translations all in the head. It is still hard to extract the key from a compromised password, since the details of the algorithm are unknown and the text sample very short.
- It is more secure than memorizing a single high-security password because, if that is compromised, then all logins are compromised. The result of the algorithm is very random-looking, which makes it hard to crack using a dictionary. Cracking by trying to guess the algorithm is hopeless, since you can use so many different possibilities for that too.
- Even if one password is compromised, that does not necessarily reveal the master key (“1234” in the above example) because the attacker does not know the exact series of steps in your algorithm. If he does, of course, he’ll get your key in no time at all, so don’t reveal your method. This is probably why Blum did not reveal his in the video.